We can now distinguish between the three possible sources of added CO2. We can immediately excludes the circulating pool, because the added CO2 contains no 14C. Of the remaining two possible sources, carbon dioxide from fossil fuels will be depleted in 13C relative to a mineral standard, while carbon dioxide from mineral sources will not. So the question is, has atmospheric carbon dioxide become more depleted in 13C over time, as its amount has risen?
Unambiguously yes. We have been following the process in real time since the late 1950s. We have extended the record back a thousand years using air trapped in ice cores, and have verified the change by examining the carbon isotopes in tree rings, which we can date by direct counting. (Tree ring carbon is of course depleted in 13C relative to atmospheric CO2, but it is depleted by a constant amount, so changes between rings match changes in the atmosphere). What we find is that over the past two hundred years, after having been nearing constant for centuries or more, atmospheric CO2 has become progressively more depleted. And the degree of depletion is exactly what we would expect if the added CO2 comes from an organic source. But remember that we have already excluded any living source, because of the absence of added 14C. That leaves fossil fuels as the only possibility.